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Math Help - L'Hospital's rule with trigs

  1. #1
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    L'Hospital's rule with trigs

    Hello all!

    I need some help with this question:

    L'Hospital's rule with trigs-picture-20.png


    the rule requires f(x)/g(x) to go to an indeterminate form, does that mean I rewrite this as a quotient?

    so lim as x-> 0 of the xth root of (sinx+cosx)

    is that right?
    Last edited by kingsolomonsgrave; November 13th 2012 at 02:19 PM.
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  2. #2
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    Re: L'Hospital's rule with trigs

    Quote Originally Posted by kingsolomonsgrave View Post
    Hello all!

    I need some help with this question:

    Click image for larger version. 

Name:	Picture 20.png 
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ID:	25693


    the rule requires f(x)/g(x) to go to an indeterminate form, does that mean I rewrite this as a quotient?

    so lim as x-> 0 of the xth root of (sinx+cosx)

    is that right?
    if
    y=\lim_{x->0}[cos(x)+sin(x)]^{1/x}

    so: ln(y)=\lim_{x->0}ln[[cos(x)+sin(x)]^{1/x}]
    Now you most use the logarithmic power rule and you will get indeterminate form: 0/0
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    Re: L'Hospital's rule with trigs

    ln(y)=lim as x->0 ln(sinx/x + cosx/x)
    am I on the right track?
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    Re: L'Hospital's rule with trigs

    Quote Originally Posted by kingsolomonsgrave View Post
    ln(y)=lim as x->0 ln(sinx/x + cosx/x)
    am I on the right track?
    This is not true you cant bring the  \frac{1}{x} "into" your ln function. You want to write  \frac{\ln( \sin(x) + \cos(x))}{x}
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